Orthogonal Matching Pursuit (OMP) is a simple, yet empirically competitive algorithm for sparse recovery. Recent developments have shown that OMP guarantees exact recovery of K-sparse signals in K iterations if the observation matrix Φ satisfies the Restricted Isometry Property (RIP) with Restricted Isometry Constant (RIC) δK+1 < 1

This paper considers the exact recovery of k-sparse signals in the noiseless setting and support recovery in the noisy case when some prior information on the support of the signals is available. This prior support consists of two parts. One part is a subset of the true support and another part is outside of the true support. For k-sparse signals x with the prior support which is composed of g ...

Generalized orthogonal matching pursuit (gOMP), also called orthogonal multi-matching pursuit, is an extension of OMP in the sense that N ≥ 1 indices are identified per iteration. In this paper, we show that if the restricted isometry constant (RIC) δNK+1 of a sensing matrix A satisfies δNK+1 < 1/ √ K/N + 1, then under a condition on the signal-to-noise ratio, gOMP identifies at least one index...

We consider the large data scattering problem for 2D and 3D cubic-quintic nonlinear Schrödinger equation in focusing-focusing regime. Our attention is firstly restricted to space, where cubic nonlinearity L2-critical. establish a new type of criterion that uniquely determined by mass initial data, which differs from classical setting based on Lyapunov functional. At end, we formulate solely mas...

Incompatibility between stability and strategy-proofness is well-known in the two-sided matching theory and this has been problems especially in designing matching rules. One possible resolution to such an impossibility result is to focus on the restricted preference domain. This paper analyzes the scope for the situation where the sets of admissible preferences for one side of the market are r...